The campaign marks five years since an International Court of Justice advisory opinion found its construction was illegal and it should be dismantled.
Since then, Oxfam says, the view of the "most distinguished international legal body has been met by inaction".
Israel says the barrier for security; Palestinians view it as a land grab.
In the report, entitled Five Years of Illegality, Oxfam details the situations of 13 Palestinian communities affected by the barrier and its associated security system of gates, buffer zones and passes.
It says displacement and exclusion caused by the barrier entails family break-up, the loss of livelihood and removal of social welfare, and "wide-ranging physical and psychological impacts, including trauma and anxiety for children".
'Dangerous'
Jeremy Hobbs, Executive Director of Oxfam International, says the testimonies are just a small insight into the "labyrinth of bans and restrictions" faced by Palestinians because of the Israeli occupation of the West Bank.
The barrier was started in 2002 and when completed will be up to 790km (490 miles) in length, with only 14% of it will running along the Green Line between Israel and the territory it has occupied since 1967. About 57% has already been completed, with 9% under construction, Oxfam says, but when completed it will divide the West Bank into three sections and completely cut off East Jerusalem, which Palestinians want as a future capital.
"No one feels safe here, especially the families living close to the Wall," says Salah Ajarma, of Aida refugee camp in Bethlehem, enclosed by a nine-metre-high concrete section of the barrier, complete with watchtowers and sniper positions.
"Our children don't have their playground any more, as it is now on the other side of the Wall. So the children play in the streets of the camp, which creates noise and prevents the older ones from studying.
"And playing in the streets is dangerous because the soldiers can fire at any moment."
Temporary
The ICJ advisory opinion of 9 July 2004 calling the barrier illegal where built on occupied land was considered a landmark by Israel's critics and received the overwhelming support in the UN General Assembly.
Israel, however, dismissed the ICJ judgement and General Assembly vote as "non-binding" and looked to its own High Court ruling that the ICJ view was flawed as it did not consider Israel's security needs.
It argues the barrier, which it calls the "security fence" is a just and necessary answer to the threat of militant attacks on its territory, such as suicide bombings.
And it says it has contributed to the virtual eradication of that threat, which took more than 200 Israeli lives in 2002.
"Since the completion of the security fence in the northern and central regions of the country, the number of successful terror attacks inside Israel has dropped almost to zero," an Israeli military spokesman said.
Oxfam, and other critics, have given little credence to Israel's assertion that the barrier is a temporary measure.
They argue that too much has already been invested in it by the government, and the pattern of settlements Israel wants to keep permanently over the Green Line reveals the barrier's purpose, they say.
It incorporates about 90% of the Israeli settler population in the occupied West Bank and East Jerusalem as well as "valuable agricultural and substantial water resources", according to Oxfam.
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